Unfortunately the hard limit is set to 1024 so you have to increase
soft limit and hard limit. You should probably set soft limit to 2048 and
hard limit to 8192

Right. I've created an /etc/initscript, exactly like the sample that's
described in "man initscript". That should fix things.

I'm still worried, though: a recent "lsof -i| grep slapd" showed that
the number of open file descriptors for the refreshAndPersist
replication process was up to 1023. Surely that's not normal. Could
this be due to a file descriptor leak?